Data has been collected HANG SENG INDEX (^HSI) from yahoo finance
getSymbols("^HSI", from="2004-01-01", to=Sys.Date())‘getSymbols’ currently uses auto.assign=TRUE\
[1] "^HSI"
Warning message:
^HSI contains missing values. Some functions will not work if objects contain missing values in the middle of the series. Consider using na.omit(), na.approx(), na.fill(), etc to remove or replace them.
> chartSeries(Cl(HSI))
> ret <- dailyReturn(Cl(HSI), type='log')
Warning message:
In to_period(xx, period = on.opts[[period]], ...) :
missing values removed from data
> par(mfrow=c(2,2))
> acf(ret, main="Return ACF");
> pacf(ret, main="Return PACF");
> acf(ret^2, main="Squared return ACF");
> pacf(ret^2, main="Squared return PACF")
> par(mfrow=c(1,1))
> m=mean(ret);s=sd(ret);
> par(mfrow=c(1,2))
> hist(ret, nclass=40, freq=FALSE, main='Return histogram');curve(dnorm(x,mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> plot(density(ret), main='Return empirical distribution');curve(dnorm(x,mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> par(mfrow=c(1,1))
> library("moments", lib.loc="~/R/win-library/3.6")
Attaching package: ‘moments’
The following objects are masked from ‘package:timeDate’:
kurtosis, skewness
> kurtosis(ret)
daily.returns
12.72668
> plot(density(ret), main='Return EDF - upper tail', xlim = c(0.1, 0.2),
+ ylim=c(0,2));
> curve(dnorm(x, mean=m,sd=s), from = -0.3, to = 0.2, add=TRUE, col="red")
> plot(density(ret), xlim=c(-5*s,5*s),log='y', main='Density on log-scale')
Warning message:
In xy.coords(x, y, xlabel, ylabel, log) :
1 y value <= 0 omitted from logarithmic plot
> curve(dnorm(x, mean=m,sd=s), from=-5*s, to=5*s, log="y", add=TRUE,
+ col="red")
> qqnorm(ret);qqline(ret);
> library("rugarch", lib.loc="~/R/win-library/3.6")
Loading required package: parallel
Attaching package: ‘rugarch’
The following object is masked from ‘package:stats’:
sigma
> ret.hsi <- dailyReturn(Cl(HSI), type='log')
> chartSeries(ret.hsi)
> garch11.spec = ugarchspec(variance.model = list(model="sGARCH",garchOrder=c(1,1)), mean.model = list(armaOrder=c(0,0)))
> hsi.garch11.fit = ugarchfit(spec=garch11.spec, data=ret.hsi)
> coef(hsi.garch11.fit)
mu omega alpha1 beta1
4.901825e-04 1.552876e-06 5.928304e-02 9.312759e-01
> vcov(hsi.garch11.fit)
[,1] [,2] [,3]
[1,] 2.644461e-08 -1.163920e-10 -1.135825e-06
[2,] -1.163920e-10 -9.074665e-12 -9.114218e-08
[3,] -1.135825e-06 -9.114218e-08 -8.802228e-04
[4,] 1.249661e-06 9.971735e-08 9.720115e-04
[,4]
[1,] 1.249661e-06
[2,] 9.971735e-08
[3,] 9.720115e-04
[4,] -1.068850e-03
infocriteria(hsi.garch11.fit)
Akaike -6.049620
Bayes -6.043153
Shibata -6.049622
Hannan-Quinn -6.047324
#calculate news impact curve
newsimpact(hsi.garch11.fit)
$zy
[1] 0.0054902042 0.0052768070 0.0050677649
[4] 0.0048630778 0.0046627457 0.0044667687
[7] 0.0042751468 0.0040878799 0.0039049680
[10] 0.0037264112 0.0035522094 0.0033823626
[13] 0.0032168710 0.0030557343 0.0028989527
[16] 0.0027465261 0.0025984546 0.0024547382
[19] 0.0023153767 0.0021803704 0.0020497190
[22] 0.0019234227 0.0018014815 0.0016838953
[25] 0.0015706641 0.0014617880 0.0013572669
[28] 0.0012571009 0.0011612899 0.0010698340
[31] 0.0009827331 0.0008999873 0.0008215965
[34] 0.0007475607 0.0006778800 0.0006125543
[37] 0.0005515837 0.0004949681 0.0004427076
[40] 0.0003948021 0.0003512517 0.0003120563
[43] 0.0002772159 0.0002467306 0.0002206003
[46] 0.0001988251 0.0001814049 0.0001683398
[49] 0.0001596297 0.0001552747 0.0001552747
[52] 0.0001596297 0.0001683398 0.0001814049
[55] 0.0001988251 0.0002206003 0.0002467306
[58] 0.0002772159 0.0003120563 0.0003512517
[61] 0.0003948021 0.0004427076 0.0004949681
[64] 0.0005515837 0.0006125543 0.0006778800
[67] 0.0007475607 0.0008215965 0.0008999873
[70] 0.0009827331 0.0010698340 0.0011612899
[73] 0.0012571009 0.0013572669 0.0014617880
[76] 0.0015706641 0.0016838953 0.0018014815
[79] 0.0019234227 0.0020497190 0.0021803704
[82] 0.0023153767 0.0024547382 0.0025984546
[85] 0.0027465261 0.0028989527 0.0030557343
[88] 0.0032168710 0.0033823626 0.0035522094
[91] 0.0037264112 0.0039049680 0.0040878799
[94] 0.0042751468 0.0044667687 0.0046627457
[97] 0.0048630778 0.0050677649 0.0052768070
[100] 0.0054902042
$zx
[1] -0.300000000 -0.293939394 -0.287878788
[4] -0.281818182 -0.275757576 -0.269696970
[7] -0.263636364 -0.257575758 -0.251515152
[10] -0.245454545 -0.239393939 -0.233333333
[13] -0.227272727 -0.221212121 -0.215151515
[16] -0.209090909 -0.203030303 -0.196969697
[19] -0.190909091 -0.184848485 -0.178787879
[22] -0.172727273 -0.166666667 -0.160606061
[25] -0.154545455 -0.148484848 -0.142424242
[28] -0.136363636 -0.130303030 -0.124242424
[31] -0.118181818 -0.112121212 -0.106060606
[34] -0.100000000 -0.093939394 -0.087878788
[37] -0.081818182 -0.075757576 -0.069696970
[40] -0.063636364 -0.057575758 -0.051515152
[43] -0.045454545 -0.039393939 -0.033333333
[46] -0.027272727 -0.021212121 -0.015151515
[49] -0.009090909 -0.003030303 0.003030303
[52] 0.009090909 0.015151515 0.021212121
[55] 0.027272727 0.033333333 0.039393939
[58] 0.045454545 0.051515152 0.057575758
[61] 0.063636364 0.069696970 0.075757576
[64] 0.081818182 0.087878788 0.093939394
[67] 0.100000000 0.106060606 0.112121212
[70] 0.118181818 0.124242424 0.130303030
[73] 0.136363636 0.142424242 0.148484848
[76] 0.154545455 0.160606061 0.166666667
[79] 0.172727273 0.178787879 0.184848485
[82] 0.190909091 0.196969697 0.203030303
[85] 0.209090909 0.215151515 0.221212121
[88] 0.227272727 0.233333333 0.239393939
[91] 0.245454545 0.251515152 0.257575758
[94] 0.263636364 0.269696970 0.275757576
[97] 0.281818182 0.287878788 0.293939394
[100] 0.300000000
$yexpr
expression(sigma[t]^2)
$xexpr
expression(epsilon[t - 1])
#obtain the residuals\
residuals(msft.garch11.fit)
///////
signbias(hsi.garch11.fit)
t-value prob sig
Sign Bias 0.1171965 9.067105e-01
Negative Sign Bias 2.4015250 1.637379e-02 **
Positive Sign Bias 3.3608760 7.844921e-04 ***
Joint Effect 32.1001392 4.985218e-07 ***
#unconditional (long-run) variance
> uncvariance(hsi.garch11.fit)
[1] 0.0001644812\
#unconditional (long-run) mean
uncmean(hsi.garch11.fit)
[1] 0.0004901825
ni.garch11 <- newsimpact(hsi.garch11.fit)
> plot(ni.garch11$zx, ni.garch11$zy, type="l", lwd=2, col="blue",
+ main="GARCH(1,1) - News Impact", ylab=ni.garch11$yexpr, xlab=ni.garch11$xexpr)
> egarch11.spec = ugarchspec(variance.model = list(model="eGARCH",garchOrder=c(1,1)), mean.model = list(armaOrder=c(0,0)))
> hsi.egarch11.fit = ugarchfit(spec=egarch11.spec, data=ret.hsi)
> coef(hsi.egarch11.fit)
mu omega alpha1
0.0002988673 -0.1349264062 -0.0556000850
beta1 gamma1
0.9843495645 0.1249733123
> ni.egarch11 <- newsimpact(hsi.egarch11.fit)
> plot(ni.egarch11$zx, ni.egarch11$zy, type="l", lwd=2, col="blue",
+ main="EGARCH(1,1) - News Impact",
+ ylab=ni.egarch11$yexpr, xlab=ni.egarch11$xexpr)
> ni.tgarch11 <- newsimpact(hsi.tgarch11.fit)
Error in newsimpact(hsi.tgarch11.fit) :
object 'hsi.tgarch11.fit' not found
> tgarch11.spec = ugarchspec(variance.model = list(model="fGARCH",submodel="TGARCH", garchOrder=c(1,1)),
+ mean.model = list(armaOrder=c(0,0)))
> hsi.tgarch11.fit = ugarchfit(spec=tgarch11.spec, data=ret.hsi)
> coef(hsi.tgarch11.fit)
mu omega alpha1 beta1
0.0002866974 0.0002251146 0.0673026379 0.9297468601
eta11
0.5022077363
> garch11.sim = ugarchpath(garch11.spec, n.sim=1000)
> hsi.garch11.fit = ugarchfit(spec=garch11.spec, data=ret.hsi, out.sample=20)
> hsi.garch11.fcst = ugarchforecast(hsi.garch11.fit, n.ahead=10,n.roll=10)
plot(hsi.garch11.fcst, which='all')
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